According to the Webster's 1913 accessible frim KDE thanks to kdict, one of the meanings for idiom is
the syntactical or structural form peculiar to any
language.

I think that syntactical/structural forms are the way of capturing
in syntax recurrent programmatic patterns so they stand out.
So a language that captures patterns syntactically absent from other languages is certainly idiomatic. Perl is very aggressive in
capturing patterns with its syntax so it is certainly idiomatic.
A language can also be very idiomatic by its very repetitive syntax like Lisp and its "clipped nails". I would use the expression syntactically idiotic here to qualify Lisp.

idiom goes beyond syntactical or structural form.
Here are two definitions from the OED (the second
and third major ones; using the 1971 compact
edition):

the specific character, property, or genius of any
language; the manner of expression which is
natural or peculiar to it.

a form of expression, grammatical construction,
phrase, etc., peculiar to a language; a
peculiarity of phraseology approved by the usage
of a language, and often having a significance
other than its grammatical or logical one

The first definition there, applied to Perl, might
be things like using $_ and @_ to write concisely
(Effective Perl Programming item 7). The second
definition would mean things like
while (<FH>) { do_stuff } (although
technically that is approved by the design, rather
than the usage, of the language) or perhaps things
like naming conventions. A non-Perl example would
be Hungarian Notation in C++. The Perl community
has things like that too.

Stuff like the Schwartzian
Transform could be considered idiomatic also,
or the practice of returning undef for false
(which, incidentally, will change in Perl6).